/* -*-c-*-
*
- * $Id: mp-arith.c,v 1.11 2002/10/06 22:52:50 mdw Exp $
+ * $Id: mp-arith.c,v 1.18 2004/04/08 01:36:15 mdw Exp $
*
* Basic arithmetic on multiprecision integers
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: mp-arith.c,v $
- * Revision 1.11 2002/10/06 22:52:50 mdw
- * Pile of changes for supporting two's complement properly.
- *
- * Revision 1.10 2001/04/03 19:36:05 mdw
- * Add some simple bitwise operations so that Perl can use them.
- *
- * Revision 1.9 2000/10/08 15:48:35 mdw
- * Rename Karatsuba constants now that we have @gfx_kmul@ too.
- *
- * Revision 1.8 2000/10/08 12:02:21 mdw
- * Use @MP_EQ@ instead of @MP_CMP@.
- *
- * Revision 1.7 2000/06/22 19:02:53 mdw
- * New function @mp_odd@ to extract powers of two from an integer. This is
- * common code from the Rabin-Miller test, RSA key recovery and modular
- * square-root extraction.
- *
- * Revision 1.6 2000/06/17 11:45:09 mdw
- * Major memory management overhaul. Added arena support. Use the secure
- * arena for secret integers. Replace and improve the MP management macros
- * (e.g., replace MP_MODIFY by MP_DEST).
- *
- * Revision 1.5 1999/12/22 15:54:41 mdw
- * Adjust Karatsuba parameters. Calculate destination size better.
- *
- * Revision 1.4 1999/12/13 15:35:16 mdw
- * Slightly different rules on memory allocation.
- *
- * Revision 1.3 1999/12/11 10:57:43 mdw
- * Karatsuba squaring algorithm.
- *
- * Revision 1.2 1999/12/10 23:18:39 mdw
- * Change interface for suggested destinations.
- *
- * Revision 1.1 1999/11/17 18:02:16 mdw
- * New multiprecision integer arithmetic suite.
- *
- */
-
/*----- Header files ------------------------------------------------------*/
#include "mp.h"
/*----- Main code ---------------------------------------------------------*/
-/* --- @mp_lsl@, @mp_lsr@ --- *
+/* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- *
*
* Arguments: @mp *d@ = destination
* @mp *a@ = source
* @size_t n@ = number of bits to move
*
* Returns: Result, @a@ shifted left or right by @n@.
+ *
+ * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced
+ * on the right with ones instead of zeroes: it's used
+ * internally by @mp_lsl2c@, though it may be useful on its
+ * own.
*/
mp *mp_lsl(mp *d, mp *a, size_t n)
return (d);
}
+mp *mp_lslc(mp *d, mp *a, size_t n)
+{
+ MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f);
+ mpx_lslc(d->v, d->vl, a->v, a->vl, n);
+ d->f = a->f & (MP_NEG | MP_BURN);
+ MP_SHRINK(d);
+ return (d);
+}
+
mp *mp_lsr(mp *d, mp *a, size_t n)
{
MP_DEST(d, MP_LEN(a), a->f);
if (!(a->f & MP_NEG))
return (mp_lsl(d, a, n));
d = mp_not2c(d, a);
- d = mp_lsl(d, d, n);
+ d = mp_lslc(d, d, n);
d = mp_not2c(d, d);
return (d);
}
/* --- @mp_testbit@ --- *
*
* Arguments: @mp *x@ = a large integer
- * @size_t n@ = which bit to test
+ * @unsigned long n@ = which bit to test
*
* Returns: Nonzero if the bit is set, zero if not.
*/
-int mp_testbit(mp *x, size_t n)
+int mp_testbit(mp *x, unsigned long n)
{
- size_t o;
if (n > MPW_BITS * MP_LEN(x))
return (0);
- o = n / MPW_BITS;
- n %= MPW_BITS;
- return ((x->v[o] >> n) & 1);
+ return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u);
}
/* --- @mp_testbit2c@ --- *
*
* Arguments: @mp *x@ = a large integer
- * @size_t n@ = which bit to test
+ * @unsigned long n@ = which bit to test
*
* Returns: Nonzero if the bit is set, zero if not. Fakes up two's
* complement representation.
*/
-int mp_testbit2c(mp *x, size_t n)
+int mp_testbit2c(mp *x, unsigned long n)
{
int r;
- if (x->f & MP_NEG)
+ if (!(x->f & MP_NEG))
return (mp_testbit(x, n));
x = mp_not2c(MP_NEW, x);
r = !mp_testbit(x, n);
return (r);
}
+/* --- @mp_setbit@, @mp_clearbit@ --- *
+ *
+ * Arguments: @mp *d@ = a destination
+ * @mp *x@ = a large integer
+ * @unsigned long n@ = which bit to modify
+ *
+ * Returns: The argument @x@, with the appropriate bit set or cleared.
+ */
+
+mp *mp_setbit(mp *d, mp *x, unsigned long n)
+{
+ size_t rq;
+
+ rq = n + MPW_BITS; rq -= rq % MPW_BITS;
+ if (d != x) {
+ if (d) MP_DROP(d);
+ d = MP_COPY(x);
+ }
+ MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
+ d->v[n/MPW_BITS] |= 1 << n%MPW_BITS;
+ return (d);
+}
+
+mp *mp_clearbit(mp *d, mp *x, unsigned long n)
+{
+ size_t rq;
+
+ rq = n + MPW_BITS; rq -= rq % MPW_BITS;
+ if (d != x) {
+ if (d) MP_DROP(d);
+ d = MP_COPY(x);
+ }
+ MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
+ d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS);
+ return (d);
+}
+
+/* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
+ *
+ * Arguments: @mp *d@ = a destination
+ * @mp *x@ = a large integer
+ * @unsigned long n@ = which bit to modify
+ *
+ * Returns: The argument @x@, with the appropriate bit set or cleared.
+ * Fakes up two's complement representation.
+ */
+
+mp *mp_setbit2c(mp *d, mp *x, unsigned long n)
+{
+ if (!(x->f & MP_NEG))
+ return mp_setbit(d, x, n);
+ d = mp_not2c(d, x);
+ d = mp_clearbit(d, d, n);
+ d = mp_not2c(d, d);
+ return (d);
+}
+
+mp *mp_clearbit2c(mp *d, mp *x, unsigned long n)
+{
+ if (!(x->f & MP_NEG))
+ return mp_clearbit(d, x, n);
+ d = mp_not2c(d, x);
+ d = mp_setbit(d, d, n);
+ d = mp_not2c(d, d);
+ return (d);
+}
+
/* --- @mp_eq@ --- *
*
* Arguments: @const mp *a, *b@ = two numbers
return (+1);
}
+/* --- @mp_neg@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @mp *a@ = argument
+ *
+ * Returns: The negation of the argument.
+ *
+ * Use: Negates its argument.
+ */
+
+mp *mp_neg(mp *d, mp *a)
+{
+ /* --- Surprising amounts of messing about required --- */
+
+ MP_SHRINK(a);
+ MP_COPY(a);
+ if (d)
+ MP_DROP(d);
+ if (a->v == a->vl)
+ return (a);
+ MP_DEST(a, MP_LEN(a), a->f);
+ a->f ^= MP_NEG;
+ return (a);
+}
+
/* --- @mp_bitop@ --- *
*
* Arguments: @mp *d@ = destination
\
mp *mp_bit##string(mp *d, mp *a, mp *b) \
{ \
- MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), a->f | b->f); \
+ MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \
mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \
d->f = (a->f | b->f) & MP_BURN; \
MP_SHRINK(d); \
MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
} else {
- size_t m = 2 * MAX(MP_LEN(a), MP_LEN(b)) + 2;
+ size_t m = MAX(MP_LEN(a), MP_LEN(b));
mpw *s;
- MP_DEST(d, m, a->f | b->f | MP_UNDEF);
- m += MPK_SLOP;
- s = mpalloc(d->a, m);
- mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m);
+ MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF);
+ s = mpalloc(d->a, 5 * m);
+ mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m);
mpfree(d->a, s);
}
size_t m = MP_LEN(a);
a = MP_COPY(a);
- MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF);
if (m > MPK_THRESH) {
mpw *s;
- m = 2 * (m + 1) + MPK_SLOP;
- s = mpalloc(d->a, m);
- mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + m);
+ MP_DEST(d, 3 * m, a->f | MP_UNDEF);
+ s = mpalloc(d->a, 5 * m);
+ mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m);
mpfree(d->a, s);
- } else
+ } else {
+ MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF);
mpx_usqr(d->v, d->vl, a->v, a->vl);
+ }
d->f = a->f & MP_BURN;
MP_SHRINK(d);
MP_DROP(a);
if (r)
MP_DROP(r);
r = a;
- MP_DEST(r, MP_LEN(a) + 2, a->f | b->f);
+ MP_DEST(r, MAX(MP_LEN(a), MP_LEN(b)) + 2, a->f | b->f);
/* --- Fix up the quotient too --- */
return (ok);
}
+static int tset(dstr *v)
+{
+ mp *a = *(mp **)v[0].buf;
+ unsigned long n = *(unsigned long *)v[1].buf;
+ mp *r = *(mp **)v[2].buf;
+ mp *c;
+ int ok = 1;
+
+ c = mp_setbit2c(MP_NEW, a, n);
+ if (!MP_EQ(c, r)) {
+ ok = 0;
+ fprintf(stderr, "\n***setbit (set) failed");
+ fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
+ fprintf(stderr, "\n*** n = %lu", n);
+ fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
+ fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
+ fputc('\n', stderr);
+ }
+ if (!mp_testbit2c(r, n)) {
+ ok = 0;
+ fprintf(stderr, "\n***setbit (test) failed");
+ fprintf(stderr, "\n*** n = %lu", n);
+ fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
+ fputc('\n', stderr);
+ }
+ mp_drop(a);
+ mp_drop(r);
+ mp_drop(c);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+static int tclr(dstr *v)
+{
+ mp *a = *(mp **)v[0].buf;
+ unsigned long n = *(unsigned long *)v[1].buf;
+ mp *r = *(mp **)v[2].buf;
+ mp *c;
+ int ok = 1;
+
+ c = mp_clearbit2c(MP_NEW, a, n);
+ if (!MP_EQ(c, r)) {
+ ok = 0;
+ fprintf(stderr, "\n***clrbit (set) failed");
+ fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
+ fprintf(stderr, "\n*** n = %lu", n);
+ fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
+ fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
+ fputc('\n', stderr);
+ }
+ if (mp_testbit2c(r, n)) {
+ ok = 0;
+ fprintf(stderr, "\n***clrbit (test) failed");
+ fprintf(stderr, "\n*** n = %lu", n);
+ fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
+ fputc('\n', stderr);
+ }
+ mp_drop(a);
+ mp_drop(c);
+ mp_drop(r);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+static int tneg(dstr *v)
+{
+ mp *a = *(mp **)v[0].buf;
+ mp *r = *(mp **)v[1].buf;
+ int ok = 1;
+ mp *n = mp_neg(MP_NEW, a);
+ if (!MP_EQ(r, n)) {
+ ok = 0;
+ fprintf(stderr, "\n*** neg failed\n");
+ fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
+ fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
+ fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
+ fputc('\n', stderr);
+ }
+ mp_drop(n);
+ n = mp_neg(a, a);
+ if (!MP_EQ(r, n)) {
+ ok = 0;
+ fprintf(stderr, "\n*** neg failed\n");
+ fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10);
+ fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
+ fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
+ fputc('\n', stderr);
+ }
+ mp_drop(a);
+ mp_drop(r);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
static int todd(dstr *v)
{
mp *a = *(mp **)v[0].buf;
mp_drop(a);
mp_drop(rt);
mp_drop(t);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
return (ok);
}
{ "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } },
{ "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } },
{ "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } },
+ { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } },
+ { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } },
{ "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
{ "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
{ "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
{ "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
{ "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } },
{ "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } },
+ { "neg", tneg, { &type_mp, &type_mp, 0 } },
{ 0, 0, { 0 } },
};
projects / u / mdw / catacomb / blobdiff